8 problems

Ferromagnetic Ordering of Energy Levels conjecture. All ferromagnetic Heisenberg models have the FOEL property: if $S'<S$, then

Let $L$ be the sector label and let $\varepsilon_m$ denote the quantity introduced in the paper for sector $m$. Ground-state energy ordering conjecture. … for all $m$ such that…

High-temperature exponential clustering conjecture. There exist $\beta^*$, $C_\mathrm{Cov}$, $c_\mathrm{Cov}>0$, and $n\in\mathbb{N}$ such that, for every $\beta<\beta^*$ and every…

Stable SPT classification group-structure conjecture. The operation $*$ is well defined, independently of the representatives, and makes $S$ an abelian group.

Consider a $d$-dimensional hypercubic lattice with translation-invariant Hamiltonians $H$ and $V$. For a sequence of lattices of increasing size, let $H(B)$ be the solution of the…

Let $H$ be the Hamiltonian in the paper's equation (Hamiltonian), and let $\widetilde{H}$ be its extended Hamiltonian in equation (HamiltonianExtended). A ladder may be closed or o…

Let $\Phi_0$ and $\Phi_1$ be two translation-invariant finite-range interactions. For $i=0,1$, suppose there are integers $l_i$ and $r_i$ such that … Here ${\mathcal S}_i^\Gamma$ d…

Let $J_0,J_1>0$, and let $\{\sigma_k\}$ be the sequence of spectra whose Hausdorff limit is studied in the paper. Let $B_\infty(J_0,J_1)$ denote the limiting spectrum when this lim…